document.write( "Question 849769: I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why.
\n" ); document.write( "(rad of 4-x PLUS the rad of x+6) all equal to 4 \n" ); document.write( "

Algebra.Com's Answer #511727 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why.
\n" ); document.write( "(rad of 4-x PLUS the rad of x+6) all equal to 4
\n" ); document.write( "----------
\n" ); document.write( "sqrt(4-x) + sqrt(x+6) = 4
\n" ); document.write( "--------
\n" ); document.write( "Square both sides to get:
\n" ); document.write( "(4-x) + (x+6) + 2sqrt[(4-x)(x+6)] = 16
\n" ); document.write( "-----
\n" ); document.write( "2sqrt(-x^2-2x+24) = 6
\n" ); document.write( "----
\n" ); document.write( "sqrt(-x^2-2x+24) = 3
\n" ); document.write( "Square both sides to get:
\n" ); document.write( "-x^2-2x+24 = 9
\n" ); document.write( "---
\n" ); document.write( "x^2 + 2x - 15 = 0
\n" ); document.write( "----
\n" ); document.write( "Factor:
\n" ); document.write( "(x+5)(x-3) = 0
\n" ); document.write( "x = 3 or x = -5
\n" ); document.write( "----
\n" ); document.write( "Neither is extraneous.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "====================== \n" ); document.write( "

\n" );